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An interface problem for a Sierpinski and a Vicsek fractal
Author(s) -
Metz Volker,
Grabner Peter
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410566
Subject(s) - sierpinski triangle , fractal , intersection (aeronautics) , mathematics , interface (matter) , lipschitz continuity , range (aeronautics) , combinatorics , mathematical analysis , pure mathematics , physics , thermodynamics , materials science , pulmonary surfactant , gibbs isotherm , aerospace engineering , engineering , composite material
We suggest a flexible way to study the self‐similar interface of two different fractals. In contrast to previous methods the participating energies are modified in the neighborhood of the intersection of the fractals. In the example of the Vicsek snowflake and the 3‐gasket, a variant of the Sierpinski gasket, we calculate the admissible transition constants via the “Short‐cut Test”. The resulting range of values is reinterpreted in terms of traces of Lipschitz spaces on the intersection. This allows us to describe the interface effects of different transition constants and indicates the techniques necessary to generalize the present interface results. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)